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SCENARIO 13-4
a Real Estate Builder Wishes to Determine How

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SCENARIO 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size).House size is measured in hundreds of square feet and income is measured in thousands of dollars.The builder randomly selected 50 families and ran the multiple regression.Partial Microsoft Excel output is provided below:  Regression Statistics  Multiple R 0.8479 R Square 0.7189 Adjusted R Square 0.7069 Standard Error 17.5571 Observations 50\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.8479 \\\text { R Square } & 0.7189 \\\text { Adjusted R Square } & 0.7069 \\\text { Standard Error } & 17.5571 \\\text { Observations } & 50\\\hline \end{array}

 ANOVA \text { ANOVA }
df SS MSF Significance F Regression 37043.323618521.66180.0000 Residual 14487.7627308.2503 Total 4951531.0863\begin{array}{lrrrrr} & d f & \text { SS } & {M S} & F & \text { Significance } F \\\hline \text { Regression } & & & 37043.3236 & 18521.6618 & 0.0000 \\\text { Residual } & & 14487.7627 & 308.2503 & \\\text { Total } & & 49 & 51531.0863 & &\end{array}

 Coefficients  Standard Error t Stat  P-value  Intercept 5.51467.22730.76300.4493 Income 0.42620.039210.86680.0000 Size 5.54371.69493.27080.0020\begin{array}{lrrrr}\hline & \text { Coefficients } & \text { Standard Error } &{t \text { Stat }} & \text { P-value } \\\hline \text { Intercept } & -5.5146 & 7.2273 & -0.7630 & 0.4493 \\\text { Income } & 0.4262 & 0.0392 & 10.8668 & 0.0000 \\\text { Size } & 5.5437 & 1.6949 & 3.2708 & 0.0020\\\hline \end{array}

 Also SSR(X1X2)=36400.6326 and SSR(X2X1)=3297.7917\text { Also } \operatorname{SSR}\left(X_{1} \mid X_{2}\right)=36400.6326 \text { and } \operatorname{SSR}\left(X_{2} \mid X_{1}\right)=3297.7917


-Referring to SCENARIO 13-4, _% of the variation in the house size can be explained by the variation in the family size while holding the family income constant.

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